Factorization in commutative Banach algebras

Dales, G. and Feinstein, J. F. and Pham, Hung (2020) Factorization in commutative Banach algebras. Studia Mathematica. ISSN 0039-3223 (In Press)

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Abstract

Let A be a (non-unital) commutative Banach algebra. We consider when A has a variety of factorization properties: we list the (obvious) implications between these properties, and then consider whether any of these implications can be reversed in various classes of commutative Banach algebras. We summarize the known counter-examples to these possible reverse implications, and add further counter-examples. Some results are used to show the existence of a large family of prime ideals in each non-zero, commutative, radical Banach algebra with a dense set of products.

Item Type:
Journal Article
Journal or Publication Title:
Studia Mathematica
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
147191
Deposited By:
Deposited On:
08 Sep 2020 15:35
Refereed?:
Yes
Published?:
In Press
Last Modified:
20 Sep 2020 06:05